Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ Exercise 9.2 Question 1: Find the sum of odd integers from 1 to 2001. Solution 1: The odd integers from 1 to 2001 are 1, 3, 5 …… 1999, 2001. This sequence forms an A.P. Here, first term, Common difference, d 2 Here, a 1 a n 1 d 2001 1 n 1 2 2001 2n 2 2000 n 1001 n Sn 2a n 1 d 2 S 1001 2 1 1001 1 2 n 2 1001 2 1000 2 2 100**11**001 1002001 Thus, the sum of odd numbers from 1 to 2001 is 1002001. Question 2: Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5. Solution 2: The natural numbers lying between 100 and 1000, which are multiples of 5, are 105, **11**0, …. 995. Here, a 105 and a n 1 d 995 d 5 105 n 1 5 995 n 1 5 995 105 890 n1 178 n 179 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ 179 S n 2 105 179 1 5 2 179 2 105 178 5 2 179 105 89 5 179 105 445 179 550 98450 Thus, the sum of all natural numbers lying between 100 and 1000, which are multiples of 5, 98450. Question 3: In an A.P, the first term is 2 and the sum of the first fiver terms is one-fourth of the next fiver terms. Show that 20 th term is **11**2. Solution 3: First term = 2 Let d be the common different of the A.P. Therefore, the A.P. is 2, 2 , 2 2 , 2 3 ... Sum of first five terms Sum of next five terms According to the given condition, 1 10 10d 10 35d 4 40 40d 10 35d 30 5d d 6 d d d 10 10d 10 35d a20 a 20 1 d 2 19 6 2 **11**4 **11**2 Thus, the 20 th of the A.P. is **11**2. Question 4: How many terms of the A.P. Solution 4: **11** 6, , 5 , ….. are needed to give the sum 25? 2 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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